Download 4-2 Triangle Congruence by SSS and SAS

4-2 TRIANGLE CONGRUENCE BY SSS AND SAS (p. 186-192)
The investigation can be skipped.
In the previous section, we learned that if two triangles have three pairs of congruent
corresponding angles and three pairs of congruent corresponding sides, then the triangles
are congruent. We are basically satisfying the definition of congruent triangles.
Fortunately, you do not need to know or show that all six pairs of corresponding parts are
congruent in order to prove that two triangles are congruent. If you know that three
special pairs of corresponding parts are congruent, then the two triangles are also
congruent.
Postulate 4-1 Side-Side-Side (SSS) Postulate
If the three sides of one triangle are congruent to the three sides of another
triangle, then the two triangles are congruent.
Example: Sketch two triangles and use tick marks to demonstrate the SSS Postulate.
Example: It is given that DE  DG and F is the midpoint of EG. Write a paragraph,
two-column, or flow proof to prove that DEF  DGF.
D
E
F
G
The word included is often used when referring to angles and sides of a triangle.
Included means contained or inserted between two objects.
Example: Sketch a triangle and demonstrate the concepts of an included side and an
included angle.
Postulate 4-2 Side-Angle-Side (SAS) Postulate
If two sides and the included angle of one triangle are congruent to two sides and
the included angle of another triangle, then the two triangles are congruent.
Example: Sketch two triangles and use tick marks to demonstrate the SAS Postulate.
Example:
M
P
O
N
It is given that MN  PO.
What other information do you need to know in order to prove MNO  PON by
SSS?
What other information do you need to know in order to prove MNO  PON by
SAS?
Do 2 on p. 188.
Do 3 on p. 188.
Homework p. 189-192: 2,4,6,7,12-14,16,21,24,27,33,34,41,45,46,53,56
34. Sketch one triangle inside a second triangle with two parallel sides.
C
D
A
41. Use
E
B
lines  alt. int. s  and SAS.